LinearSemilogGrowthSpline without knotsSpline with knotsARIMA
(Intercept)309.718 ****-61.807     4.679 ****-4.427     79.837          
(34.859)    (93.889)    (0.140)    (62.400)    (153.383)         
Day0.105              0.001 ***                        
(0.116)             (0.000)                           
log(Day)         75.814 ****                                
         (17.539)                                    
bs(Day, knots = NULL)1                           518.671 ***               
                           (180.305)                  
bs(Day, knots = NULL)2                           924.409 ****              
                           (114.445)                  
bs(Day, knots = NULL)3                           -73.495                   
                           (98.521)                  
bs(Day, knots = c(30, 247, 420))1                                    -238.760          
                                    (189.563)         
bs(Day, knots = c(30, 247, 420))2                                    623.211 ****     
                                    (163.042)         
bs(Day, knots = c(30, 247, 420))3                                    -176.185          
                                    (190.514)         
bs(Day, knots = c(30, 247, 420))4                                    1237.844 ****     
                                    (169.846)         
bs(Day, knots = c(30, 247, 420))5                                    -925.546 ****     
                                    (178.335)         
bs(Day, knots = c(30, 247, 420))6                                    693.659 ****     
                                    (178.836)         
ar1                                             0.237 
                                             (0.106)
ar2                                             -0.841 
                                             (0.088)
ar3                                             -0.127 
                                             (0.107)
ar4                                             -0.413 
                                             (0.047)
ar5                                             -0.448 
                                             (0.055)
ma1                                             -0.945 
                                             (0.110)
ma2                                             1.038 
                                             (0.162)
ma3                                             -0.456 
                                             (0.149)
ma4                                             0.366 
                                             (0.093)
nobs521         521         521         521         521         520     
r.squared0.002     0.035     0.013     0.189     0.374          
adj.r.squared-0.000     0.033     0.011     0.185     0.367          
sigma397.258     390.607     1.601     358.640     316.081     140.204 
statistic0.830     18.685     6.910     40.269     51.188          
p.value0.363     0.000     0.009     0.000     0.000          
df1.000     1.000     1.000     3.000     6.000          
logLik-3856.235     -3847.437     -983.504     -3801.948     -3734.618     -3304.902 
AIC7718.469     7700.875     1973.009     7613.895     7485.236     6629.804 
BIC7731.236     7713.642     1985.776     7635.174     7519.282     6672.342 
deviance81905514.761     79185735.475     1330.515     66497947.233     51352160.074          
df.residual519.000     519.000     519.000     517.000     514.000          
nobs.1521.000     521.000     521.000     521.000     521.000     520.000 
**** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1.
Linear Semilog Growth Spline with knots Spline without knots Smooth spline ARIMA
Absolute Error 150000 150000 170000 120000 140000 39000 42000
Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf
Accuracy 0 0 0 0 0 0 0
Adjusted R Square -0.00033 0.033 0.011 0.37 0.18 0 0
Akaike’s Information Criterion AIC 7700 7700 2000 7500 7600 0 6600
Allen’s Prediction Sum-Of-Squares (PRESS, P-Square) 0 0 0 0 0 0 0
Area under the ROC curve (AUC) 0.0087 0.0087 0.0087 0.14 0.04 0.0087 0.02
Average Precision at k 0 0 0 0 0 0 0
Bias 0.0000000000000089 -0.000000000000035 330 -0.0000000000000047 -0.000000000000036 0.00000000000011 2.5
Brier score 200000 200000 300000 100000 100000 20000 20000
Classification Error 1 1 1 1 1 1 1
F1 Score 0 0 0 0 0 0 0
fScore 0 0 0 0 0 0 0
GINI Coefficient 0.05 0.05 0.05 0.8 0.6 1 1
kappa statistic 0 0 0 0 0 0 0
Log Loss Inf Inf Inf Inf Inf Inf Inf
Mallow’s cp 2 2 2 7 4 0 0
Matthews Correlation Coefficient 0 0 0 0 0 0 0
Mean Log Loss Inf Inf Inf Inf Inf Inf Inf
Mean Absolute Error 290 280 330 230 260 74 81
Mean Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf
Mean Average Precision at k 0 0 0 0 0 0.2 0
Mean Absolute Scaled Error 3 2.9 3.4 2.3 2.7 0.76 0.84
Median Absolute Error 250 220 180 190 220 34 42
Mean Squared Error 160000 150000 270000 99000 130000 18000 19000
Mean Squared Log Error 3.2 NaN 13 NaN NaN 0.28 0.28
Model turning point error 264 264 264 241 265 248 296
Negative Predictive Value 0 0 0 0 0 0 0
Percent Bias -Inf NaN -Inf NaN NaN NaN NaN
Positive Predictive Value 0 0 0 0 0 0 0
Precision NaN NaN NaN NaN NaN NaN NaN
R Square 0.0016 0.035 0.013 0.37 0.19 0 0
Relative Absolute Error 1 0.98 1.2 0.79 0.9 0.26 0.28
Recall 310 29 4.7 9.7 10 -0.18 0.45
Root Mean Squared Error 400 390 520 310 360 140 140
Root Mean Squared Log Error 1.8 NaN 3.6 NaN NaN 0.53 0.53
Root Relative Squared Error 1 0.98 1.3 0.79 0.9 0.34 0.35
Relative Squared Error 1 0.97 1.7 0.63 0.81 0.12 0.12
Schwarz’s Bayesian criterion BIC 7700 7700 2000 7500 7600 0 6700
Sensitivity 0 0 0 0 0 0 0
specificity 0 0 0 0 0 0 0
Squared Error 82000000 79000000 140000000 51000000 66000000 9600000 10000000
Squared Log Error 1700 NaN 6700 NaN NaN 150 150
Symmetric Mean Absolute Percentage Error 0.93 0.93 1.8 0.89 0.93 0.35 0.41
Sum of Squared Errors 82000000 79000000 140000000 51000000 66000000 9600000 10000000
True negative rate 0 0 0 0 0 0 0
True positive rate 0 0 0 0 0 0 0

Spline without knotsSpline with knotsARIMAQuardratic polynomialEssembled based on weightEssembled based on summed weight
(Intercept)-4.427     -5.445          -73.079     63.252  5.538     
(62.400)    (56.636)         (47.384)    (58.044) (12.629)    
bs(Day, knots = NULL)1518.671 ***                                       
(180.305)                                          
bs(Day, knots = NULL)2924.409 ****                                      
(114.445)                                          
bs(Day, knots = NULL)3-73.495                                           
(98.521)                                          
bs(Day, knots = BREAKS)1         12.816                                  
         (109.491)                                 
bs(Day, knots = BREAKS)2         5.594                                  
         (70.929)                                 
bs(Day, knots = BREAKS)3         856.945 ****                             
         (81.316)                                 
bs(Day, knots = BREAKS)4         153.515 **                               
         (69.095)                                 
bs(Day, knots = BREAKS)5         241.337 ***                              
         (75.755)                                 
bs(Day, knots = BREAKS)6         -145.933 **                               
         (71.460)                                 
bs(Day, knots = BREAKS)7         2160.088 ****                             
         (71.855)                                 
bs(Day, knots = BREAKS)8         -515.379 ****                             
         (75.125)                                 
bs(Day, knots = BREAKS)9         452.093 ****                             
         (85.368)                                 
bs(Day, knots = BREAKS)10         -209.867 **                               
         (81.457)                                 
bs(Day, knots = BREAKS)11         583.000 ****                             
         (80.978)                                 
ar1                  0.237                         
                  (0.106)                        
ar2                  -0.841                         
                  (0.088)                        
ar3                  -0.127                         
                  (0.107)                        
ar4                  -0.413                         
                  (0.047)                        
ar5                  -0.448                         
                  (0.055)                        
ma1                  -0.945                         
                  (0.110)                        
ma2                  1.038                         
                  (0.162)                        
ma3                  -0.456                         
                  (0.149)                        
ma4                  0.366                         
                  (0.093)                        
Day                       4.497 ****               
                       (0.419)                   
I(Day^2)                       -0.008 ****               
                       (0.001)                   
fitf                                -2.984  -0.187     
                                (2.954) (0.127)    
fit0f                                -1.405  -0.153     
                                (1.356) (0.234)    
fit1f                                2.360  0.755 ****
                                (2.923) (0.146)    
fitpif                                1.050  0.131     
                                (0.945) (0.235)    
fitaf                                -0.253  0.440 ****
                                (1.880) (0.065)    
fitf:fit0f                                -0.029           
                                (0.021)          
fitf:fit1f                                0.002           
                                (0.004)          
fit0f:fit1f                                0.040           
                                (0.028)          
fitf:fitpif                                0.053 *         
                                (0.030)          
fit0f:fitpif                                0.001           
                                (0.001)          
fit1f:fitpif                                -0.051           
                                (0.036)          
fitf:fitaf                                0.002           
                                (0.021)          
fit0f:fitaf                                0.007           
                                (0.013)          
fit1f:fitaf                                0.005           
                                (0.016)          
fitpif:fitaf                                -0.009           
                                (0.018)          
fitf:fit0f:fit1f                                -0.000           
                                (0.000)          
fitf:fit0f:fitpif                                -0.000           
                                (0.000)          
fitf:fit1f:fitpif                                0.000           
                                (0.000)          
fit0f:fit1f:fitpif                                0.000           
                                (0.000)          
fitf:fit0f:fitaf                                0.000           
                                (0.000)          
fitf:fit1f:fitaf                                -0.000           
                                (0.000)          
fit0f:fit1f:fitaf                                -0.000           
                                (0.000)          
fitf:fitpif:fitaf                                -0.000           
                                (0.000)          
fit0f:fitpif:fitaf                                0.000           
                                (0.000)          
fit1f:fitpif:fitaf                                0.000           
                                (0.000)          
fitf:fit0f:fit1f:fitpif                                0.000           
                                (0.000)          
fitf:fit0f:fit1f:fitaf                                0.000           
                                (0.000)          
fitf:fit0f:fitpif:fitaf                                0.000           
                                (0.000)          
fitf:fit1f:fitpif:fitaf                                0.000           
                                (0.000)          
fit0f:fit1f:fitpif:fitaf                                -0.000           
                                (0.000)          
fitf:fit0f:fit1f:fitpif:fitaf                                -0.000           
                                (0.000)          
nobs521         521         520     521         521      521         
r.squared0.189     0.863          0.186     0.901  0.894     
adj.r.squared0.185     0.860          0.182     0.894  0.893     
sigma358.640     148.456     140.204 359.137     129.184  130.062     
statistic40.269     292.116          59.021     142.799  866.924     
p.value0.000     0.000          0.000     0.000  0.000     
df3.000     11.000          2.000     31.000  5.000     
logLik-3801.948     -3338.349     -3304.902 -3803.173     -3255.458  -3272.483     
AIC7613.895     6702.698     6629.804 7614.346     6576.916  6558.966     
BIC7635.174     6758.022     6672.342 7631.369     6717.355  6588.756     
deviance66497947.233     11218017.844          66811506.045     8160628.858  8711782.329     
df.residual517.000     509.000          518.000     489.000  515.000     
nobs.1521.000     521.000     520.000 521.000     521.000  521.000     
**** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1.
Spline with knots Spline without knots Smooth spline ARIMA Quardratic polynomial Essembled equal weight Essembled on weight Essembled summed weight Essembled weight of fit
Absolute Error 45000 140000 39000 42000 130000 180000 37000 38000 180000
Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf Inf Inf
Accuracy 0 0 0 0 0 0.035 0 0 0.035
Adjusted R Square 0.86 0.18 0 0 0.18 0 0.89 0.89 0
Akaike’s Information Criterion AIC 6700 7600 0 6600 7600 0 6600 6600 0
Allen’s Prediction Sum-Of-Squares (PRESS, P-Square) 0 0 0 0 0 0 0 0 0
Area under the ROC curve (AUC) 0.0087 0.04 0.0087 0.02 0.0087 0.0087 0.076 0.0096 0.0087
Average Precision at k 0 0 0 0 0 0.5 0 0 0.5
Bias 0.0000000000000012 -0.000000000000036 0.00000000000011 2.5 0.000000000000042 340 -0.00000000000000054 -0.0000000000000015 340
Brier score 20000 100000 20000 20000 100000 300000 20000 20000 NaN
Classification Error 1 1 1 1 1 1 1 1 1
F1 Score 0 0 0 0 0 0 0 0 0
fScore 0 0 0 0 0 0 0 0 0
GINI Coefficient 1 0.6 1 1 0.5 0.9 1 1 0.9
kappa statistic 0 0 0 0 0 NaN 0 0 NaN
Log Loss Inf Inf Inf Inf Inf Inf Inf Inf Inf
Mallow’s cp 12 4 0 0 3 0 0 6 0
Matthews Correlation Coefficient 0 0 0 0 0 NaN 0 0 NaN
Mean Log Loss Inf Inf Inf Inf Inf NaN Inf Inf NaN
Mean Absolute Error 87 260 74 81 260 340 70 72 NaN
Mean Absolute Percent Error Inf Inf Inf Inf Inf Inf Inf Inf Inf
Mean Average Precision at k 0 0 0.2 0 0 0 0 0 0
Mean Absolute Scaled Error 0.89 2.7 0.76 0.84 2.6 3.5 0.72 0.74 3.5
Median Absolute Error 51 220 34 42 210 98 37 35 130
Mean Squared Error NA NA NA NA NA 270000 NA NA NaN
Mean Squared Log Error NaN NaN 0.28 0.28 NaN 28 NaN NaN 28
Model turning point error 253 265 248 296 264 281 234 282 275
Negative Predictive Value 0 0 0 0 0 0 0 0 0
Percent Bias NaN NaN NaN NaN NaN NaN -Inf NaN NaN
Positive Predictive Value 0 0 0 0 0 0 0 0 0
Precision NaN NaN NaN NaN NaN 0 NaN NaN 0
R Square 0.86 0.19 0 0 0.19 0 0.9 0.89 0
Relative Absolute Error 0.3 0.9 0.26 0.28 0.89 0.44 0.24 0.25 0.6
Recall -2.9 10 -0.18 0.45 -47 0 17 -1.6 0
Root Mean Squared Error NA NA NA NA NA 520 NA NA NaN
Root Mean Squared Log Error NaN NaN 0.53 0.53 NaN 5.3 NaN NaN 5.3
Root Relative Squared Error 0.37 0.9 0.34 0.35 0.9 1.3 0.32 0.33 1.3
Relative Squared Error 0.14 0.81 0.12 0.12 0.81 1.7 0.099 0.11 1.7
Schwarz’s Bayesian criterion BIC 6800 7600 0 6700 7600 0 6700 6600 0
Sensitivity 0 0 0 0 0 0.5 0 0 0.5
specificity 0 0 0 0 0 0 0 0 0
Squared Error 11000000 66000000 9600000 10000000 67000000 140000000 8200000 8700000 140000000
Squared Log Error NaN NaN 150 150 NaN 14000 NaN NaN 14000
Symmetric Mean Absolute Percentage Error 0.49 0.93 0.35 0.41 0.89 0.59 0.41 0.36 0.71
Sum of Squared Errors 11000000 66000000 9600000 10000000 67000000 140000000 8200000 8700000 140000000
True negative rate 0 0 0 0 0 0 0 0 0
True positive rate 0 0 0 0 0 0 0 0 0

LinearSemilogGrowth
(Intercept)309.718 ****-61.807     4.679 ****
(34.859)    (93.889)    (0.140)    
Day0.105              0.001 *** 
(0.116)             (0.000)    
log(Day)         75.814 ****         
         (17.539)             
nobs521         521         521         
r.squared0.002     0.035     0.013     
adj.r.squared-0.000     0.033     0.011     
sigma397.258     390.607     1.601     
statistic0.830     18.685     6.910     
p.value0.363     0.000     0.009     
df1.000     1.000     1.000     
logLik-3856.235     -3847.437     -983.504     
AIC7718.469     7700.875     1973.009     
BIC7731.236     7713.642     1985.776     
deviance81905514.761     79185735.475     1330.515     
df.residual519.000     519.000     519.000     
nobs.1521.000     521.000     521.000     
**** p < 0.001; *** p < 0.01; ** p < 0.05; * p < 0.1.